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In this paper we present qualitative and quantitative comparison of variousanalytical and numerical approximation methods for calculating a position ofthe early exercise boundary of the American put option paying zero dividends.First we analyze their asymptotic behavior close to expiration. In the secondpart of the paper, we introduce a new numerical scheme for computing the entireearly exercise boundary. The local iterative numerical scheme is based on asolution to a nonlinear integral equation. We compare numerical resultsobtained by the new method to those of the projected successive over relaxationmethod and the analytical approximation formula recently derived by Zhu.

Comparison of numerical and analytical approximations of the early exercise boundary of the American put option